Rendering in computer graphics systems

ABSTRACT

A graphics system has a rendering space divided into a plurality of rectangular areas, each being sub-divided into a plurality of smaller rectangular areas of a plurality of pixels. Data is received representing a tiled set of polygons to be rendered in a selected one of the rectangular areas. For each polygon, a determination is made whether that polygon is located at least partially inside a selected one of the smaller rectangular areas in the selected rectangular area. If so, which pixels of the plurality of pixels in the selected smaller rectangular area are inside the polygon are identified. Or, if that polygon is not located at least partially inside the selected smaller rectangular area, no further processing of the polygon is performed at one or more of the plurality of pixels in the smaller rectangular area.

BACKGROUND

Computer graphics systems generally comprise a geometry processing unitwhich receives data defining the geometry to be rendered and convertsthis to a set of graphics primitives (also referred to as polygons),typically triangles, which are used when rendering the image. Thesurfaces of each object are sub-divided into these graphics primitives.Each triangular primitive is defined by a set of vertices which, inturn, defines the planar surface and the extent of that surface.

There are two main families of computer graphics systems: tile-basedsystems and immediate mode systems.

In tile-based rendering systems, the display or framebuffer isconceptually subdivided into a plurality of rectangular areas, known as“tiles”, each corresponding to a (usually) predetermined number ofpixels (e.g. 32*32). For each tile, an object list is compiled whichreferences or contains (at least) the primitives in the image whichintersect, or potentially intersect, that tile. This process issometimes referred to as “tiling” or “binning”. Thus, tiles do not needto process the objects which do not intersect them. A tiling unit isoften used to improve the speed of creating the per-tile lists.

In immediate mode renderers, although scanline-order processing ofprimitives is frequently employed, some systems instead opt to dividethe screen into tiles of pixels. The rendering of each primitive is doneon a tile by tile basis, with each pixel in a tile being processedbefore progressing to the next tile. The rendering order is chosen toimprove locality of memory references e.g. the texture fetches. Notethat, with immediate mode renderers, no per-tile lists are created andeach primitive appears to be rendered immediately—although, due topipelining and parallelism, there may, of course, be a number ofprimitives being processed simultaneously.

During the rendering of the pixels (in either tile-based or immediatemode rendering systems), a graphics system will usually determine whichpixels an object intersects (also known as scan conversion) and whichobject is visible at each pixel using depth testing to find the closestobject to a view point. Texturing and shading data can then be appliedto the pixel.

Where objects are transparent, data from a frontmost object and fromobjects behind it may be required to properly texture and shade a pixel.

SUMMARY

A rendering technique for a computer graphics system is described inwhich each rectangular area (tile) is divided into smaller rectangularareas (microtiles), each comprising a plurality of pixels. Duringrendering of a tile, for each polygon associated with that tile, acoarse grain evaluation is used to identify the set of microtilescovered, wholly or partially, by the polygon. Those microtiles may bereferred to as the active microtiles. For each active microtile (andonly those microtiles), scan conversion and other rasterizationprocesses, such as depth processing, are then applied to the pixels inthat microtile. The microtiles in the active set can be processed in anyorder, or even in parallel given sufficient resources.

According to a first aspect, there is provided a method of rendering ina graphics system having a rendering space divided into a plurality ofrectangular areas and having each rectangular area sub-divided into aplurality of smaller rectangular areas each comprising a plurality ofpixels, the method comprising: receiving data representing a tiled setof polygons to be rendered in a selected one of the rectangular areas;for each polygon in the tiled set, determining whether that polygon islocated at least partially inside a selected one of the smallerrectangular areas in the selected rectangular area; and if that polygonis located at least partially inside the selected smaller rectangulararea, determining which of the plurality of pixels in the selectedsmaller rectangular area are inside the polygon, or if that polygon isnot located at least partially inside the selected smaller rectangulararea, performing no further processing of the polygon at one or more ofthe plurality of pixels in the smaller rectangular area.

Thus, the method first identifies which smaller rectangular areas(microtiles) are intersected by the polygon (i.e. fall at leastpartially inside the polygon), and then only processes those identifiedsmaller rectangular areas. Thus, the smaller rectangular areasidentified are the active microtiles. By performing the initialidentification at microtile scale, which is a relatively coarse grainevaluation, subsequent processing costs can be reduced. Relativelyinexpensive low precision calculations may be used to initially identifythose smaller rectangular areas which are intersected by the polygon.Small polygons in a large rectangular area (tile) may be dealt withefficiently; in a tile-based renderer, using larger tiles reduces thecost of the tiling and binning process. Polygons with extreme aspectratios, such as line polygons, may be dealt with more efficiently.Smaller rectangular areas (microtiles) may be processed in any order,which allows implementation of load balancing schemes in subsequentprocessing steps.

The size, number and shape of the rectangular areas and the smallerrectangular areas may be selected as desired. The size of the smallerrectangular areas may be determined by the amount of computing orsilicon resources available in a single clock cycle for the step ofdetermining which of the plurality of pixels in the selected smallerrectangular area are inside the polygon. Choosing smaller rectangularareas that are square, or nearly square, will typically result in thehighest utilisation of the parallel pixel units used to evaluate asmaller rectangular area. By using smaller rectangular areas having asquare aspect ratio, there will be relatively little disparity betweenprocessing of polygons with extreme aspect ratios at different angles oforientation.

In one example, a rectangular area (tile) of 32*32 pixels may besubdivided into 64 4*4 smaller rectangular areas (microtiles). Forexample, computing resources may be available to process one 4*4microtile per clock cycle. Therefore, in this example, a polygoncovering the entire 32*32 tile would be processed in 64 clock cycles,but a small polygon covering only one microtile would be processed inonly 1 clock cycle.

In one example, the method further comprises: receiving a plurality ofimage polygons to be rendered in the rendering space; and tiling theimage polygons to generate the tiled set of polygons by determining atleast those image polygons that are located within the selectedrectangular area.

In one example, determining whether the polygon is located at leastpartially inside the selected smaller rectangular area comprises:providing a plurality of sample points for each rectangular area, thenumber of sample points in a rectangular area being equal to the numberof smaller rectangular areas in the rectangular area and each samplepoint being located in a respective smaller rectangular area; andidentifying the sample points falling inside the polygon. In thatexample, in order for a sample point identified as falling inside thepolygon to correspond to its smaller rectangular area falling at leastpartially inside the polygon, an edge of the polygon and/or the samplepoint may be adjusted. For example, an edge of the polygon and/or thesample point may be translated. The translation may be dependent on thelocation of the sample point in the smaller rectangular area and theorientation of the edge.

Determining whether the polygon is located at least partially inside theselected smaller rectangular area may comprise: deriving a plurality ofedges from the polygon; and comparing each of the plurality of edgeswith a sample point associated with the selected smaller rectangulararea to determine whether the selected smaller rectangular area islocated wholly outside any of the edges; wherein if the selected smallerrectangular area is not located wholly outside any of the edges then thepolygon is determined to be located at least partially inside theselected smaller rectangular area.

Typical systems render convex polygons. If the sampling point for asmaller rectangular area falls inside all edges of a convex polygon (forexample, inside all three edges for a triangular polygon), we canconclude that the smaller rectangular area falls wholly or partiallywithin the polygon. The edge equation for each polygon edge is computedfrom vertex data defining the vertices of the polygon. The sample pointsprovide a low resolution grid which may be used for the coarse grainevaluation to identify the active smaller rectangular areas(microtiles). The location of each sample point in its respectivesmaller rectangular area may be selected as desired. However, all samplepoints are located in the same position in the respective smallerrectangular areas, thereby providing a regularly spaced grid of samplepoints. For example, each sample point may be located at the top leftcorner of its smaller rectangular area.

In an example, comparing each of the plurality of edges comprises:processing each of the plurality of edges to derive a plurality ofprocessed edges, wherein the processing comprises, for each edge,determining an orientation of the respective edge and applying atranslation to the respective edge in accordance with the orientation;and comparing each of the plurality of processed edges with the samplepoint.

The translation ensures that, if the sample point is found to fallinside the edge, at least a part of the selected smaller rectangulararea falls inside the edge, and if the sample point is found to falloutside the edge, the entire selected smaller rectangular area fallsoutside the edge. This avoids the possibility that the sample point isfound to fall outside the edge, but part of the selected smallerrectangular area actually falls inside the edge. This may occur forcertain sample point locations within the selected smaller rectangulararea and certain edge orientations. Thus, the translation may bedependent on the location of the sample point in the selected smallerrectangular area and the orientation of the edge. The translation may bezero in some cases.

Applying the translation to the respective edge in accordance with theorientation may comprise: applying a translation to the respective edgein one dimension, applying a translation to the respective edge in twodimensions, or applying no translation to the respective edge.

Each processed edge may be represented by a respective edge equation,and comparing each of the plurality of processed edges with the samplepoint may comprise evaluating the respective edge equation at the samplepoint and determining whether the evaluation exceeds a predeterminedthreshold.

It is possible to use the evaluation to determine whether the smallerrectangular area or the sample point falls inside or outside the edgebecause the edge equations have direction around the polygon.Determining simply whether the evaluation exceeds a predeterminedthreshold is a relatively simple calculation—more straightforward thanevaluating the actual value. The predetermined threshold may be zero, inwhich case, the determining determines whether the evaluation ispositive or negative.

The method may further comprise using the determination of whether theevaluation exceeds a predetermined threshold to determine whether thesample point is located inside or outside the processed edge.

Typically, the edge equations are directed in a clockwise directionaround the polygon. Thus, in that example, if the processed edgeequation evaluated at the sample point is positive, the smallerrectangular area with which that sample point is associated isidentified as falling inside the edge from which the processed edge wasderived and, if the processed edge equation evaluated at the samplepoint is negative, the smaller rectangular area with which that samplepoint is associated is identified as falling outside the edge from whichthe processed edge was derived. If the processed edge equation evaluatedat the sample point is zero, the sample point falls exactly on the edgefrom which the processed edge was derived. For simplicity in this coarsegrain evaluation (i.e. the initial identification of which smallerrectangular areas fall at least partially inside the polygon), therectangular area with which that sample point is associated may betreated as inside the polygon edge. The edge equation for each polygonedge may be equivalent to data defining a surface perpendicular to aviewpoint and facing towards the polygon.

In one example, if the sample point is located inside the processededge, then the smaller rectangular area, with which the sample point isassociated, is located at least partially inside the edge from which theprocessed edge was derived, and if the sample point is located outsidethe processed edge, then the smaller rectangular area, with which thesample point is associated, is located wholly outside the edge fromwhich the processed edge was derived.

Each edge equation may be of the form E(x,y)=Ax+By+C, where A, B and Care constants specific to the processed edge, and determining whetherthe evaluation exceeds a predetermined threshold may comprise comparing−Ax with By+C.

The edge equation E(x,y)=Ax+By+C for each polygon edge is computed fromvertex data defining the vertices of the polygon. x and y represent ascreen location, a pixel location or a subpixel location. Constant C maybe adjusted so that the scene origin is at the location of the top leftsample point. This increases efficiency of the processing, because themagnitude of the x and y values is smaller.

The method may further comprise outputting a first value if By+C>−Ax andoutputting a second value if By+C<−Ax, one of the first value and thesecond value indicating that the sample point is located inside theprocessed edge and the other of the first value and the second valueindicating that the sample point is located outside the processed edge.

Thus, a single output value can indicate whether the sample point islocated inside or outside the processed edge. Hence, it can bedetermined whether the selected smaller rectangular area is locatedwholly outside the edge. If the output bits for all edges of the polygonindicate that the smaller rectangular area falls inside (or partiallyinside) all edges, that rectangular area can be identified as a smallerrectangular area which falls at least partially inside the polygon.

In one example, if By+C=−Ax (i.e. if the sample point falls exactly onthe processed edge), the value which indicates that the sample pointfalls inside the processed edge may be output. That is, in this coarsegrain evaluation, it may be sufficient to treat sample points fallingexactly on an edge as inside that edge. However, in an alternativeexample, a tie-breaking rule may be applied.

Comparing −Ax with By+C for each processed edge for all sample points ina rectangular area may be performed using a plurality of comparators,each comparator associated with one sample point and one smallerrectangular area in the rectangular area. Thus, the number ofcomparators is equal to the number of sample points and smallerrectangular areas in the rectangular area. Such a plurality ofcomparators may be referred to as an array of comparators. For example,if a rectangular area (tile) of 32*32 pixels is subdivided into 64 4*4smaller rectangular areas (microtiles), 64 comparators (8*8) may beprovided. Such an array or plurality may be provided for each polygonedge. For example, if the polygons are triangles (which is typically thecase), three arrays of comparators may be provided. Alternatively, thesame array of comparators may be used sequentially for each edge.

Comparing −Ax with By+C for the processed edge may comprise reducing theprecision of “By+C” and comparing “−Ax” with the reduced precision“By+C”. By reducing the precision of the By+C expression, beforecomparing it with the −Ax expression, the cost of the comparison may bereduced. Since a comparison must be made for each processed edge againsteach sample point, a large total number of comparisons need to be made.Thus, any (even small) cost reduction in each individual comparison maysignificantly reduce the total cost.

According to a first example, the step of, for each polygon in the tiledset, determining whether that polygon is located at least partiallyinside a selected one of the smaller rectangular areas in the selectedrectangular area, is performed for all smaller rectangular areas in therectangular area in parallel for each edge of the polygon.

The comparison for all smaller rectangular areas in a given rectangulararea may be performed in a single step. In this example, if an edgeequation is provided to define each polygon edge, the edge equation iscompared with all sample points (i.e. all smaller rectangular areas) inthe rectangular area in parallel. If each edge equation is of the formE(x,y)=Ax+By+C, −Ax may be compared with By+C for all sample points inparallel.

The comparisons for all the polygon edges may be performed sequentiallyor in parallel.

According to a second example, the step of, for each polygon in thetiled set, determining whether that polygon is located at leastpartially inside a selected one of the smaller rectangular areas in theselected rectangular area, is performed in a plurality of serial steps,each serial step comprising identifying the smaller rectangular areas,of a subset of the smaller rectangular areas in the rectangular area,falling at least partially inside the polygon.

Each subset may comprise a row or column of microtiles within the tile.That is, each serial step identifies which microtile in that row orcolumn falls at least partially inside the polygon. The number of serialsteps will depend on the total number of microtiles in the tile and thenumber of microtiles in each subset. For example, if a rectangular area(tile) of 32*32 pixels is subdivided into 64 4*4 smaller rectangularareas (microtiles), each serial step may identify which microtile ineach 8 microtile row or column falls at least partially inside thepolygon, and 8 serial steps will be required for the total 64evaluations.

In this example, if an edge equation is provided to define each polygonedge, the edge equation may be compared with the sample points in thesubset of the smaller rectangular areas in parallel, then the edgeequation may be compared with the sample points in the next subset ofthe smaller rectangular areas in parallel, and so on until all thesample points are evaluated. If each edge equation is of the formE(x,y)=Ax+By+C, −Ax may be compared with By+C for all sample points in asubset in parallel, then −Ax may be compared with By+C for all samplepoints in the next subset, and so on.

The comparisons for all the polygon edges may be performed sequentiallyor in parallel.

In one example, each rectangular area is sub-divided into a plurality ofintermediate rectangular areas, each intermediate rectangular areacomprising a plurality of the smaller rectangular areas, and whereindetermining for each polygon in the tiled set, whether that polygon islocated at least partially inside the selected one of the smallerrectangular areas comprises: determining whether that polygon is locatedat least partially inside a selected one of the intermediate rectangularareas in the selected rectangular area, the selected intermediaterectangular area including the selected smaller rectangular area; and ifso, determining whether that polygon is located at least partiallyinside the selected one of the smaller rectangular areas, or if not,determining that that polygon is not located at least partially insidethe selected smaller rectangular area.

That is, an additional level of hierarchy may be used to first divideeach rectangular area (tile) into intermediate rectangular areas(“minitiles”). Each minitile in the tile may then be evaluated in turn,to identify the active microtiles within that minitile. One example uses64*64 pixel tiles, a 16*16 pixel intermediate minitile, and a 4*4microtile.

In one example, the method further comprises rasterizing those pixels inthe selected smaller rectangular area that are determined to be insidethe polygon.

According to a second aspect, there is provided a graphics system havinga rendering space divided into a plurality of rectangular areas andhaving each rectangular area sub-divided into a plurality of smallerrectangular areas each comprising a plurality of pixels, the graphicssystem comprising a processing unit configured to: receive datarepresenting a tiled set of polygons to be rendered in a selected one ofthe rectangular areas; and determine, for each polygon in the tiled set,whether that polygon is located at least partially inside a selected oneof the smaller rectangular areas in the selected rectangular area,wherein, if that polygon is located at least partially inside theselected smaller rectangular area, the processing unit is arranged todetermine which of the plurality of pixels in the selected smallerrectangular area are inside the polygon, and if that polygon is notlocated at least partially inside the selected smaller rectangular area,the processing unit is arranged to perform no further processing of thepolygon at one or more of the plurality of pixels in the smallerrectangular area.

Thus, the graphics system is arranged to identify which smallerrectangular areas (microtiles) are intersected by the polygon (i.e. fallat least partially inside the polygon), and to then only process thoseidentified smaller rectangular areas. Thus, the identified smallerrectangular areas are the active microtiles. By performing the initialidentification at microtile scale, which is a relatively coarse grainevaluation, subsequent processing costs can be reduced.

In an example, the processing unit is further configured to: receive aplurality of image polygons to be rendered in the rendering space; andtile the image polygons to generate the tiled set of polygons bydetermining at least those image polygons that are located within theselected rectangular area.

In an example, a plurality of sample points is provided for eachrectangular area, the number of sample points in a rectangular areabeing equal to the number of smaller rectangular areas in therectangular area and each sample point being located in a respectivesmaller rectangular area; and the processing unit is configured todetermine, for each polygon in the tiled set, whether that polygon islocated at least partially inside a selected one of the smallerrectangular areas in the selected rectangular area by identifying thesample points falling inside the polygon. The sample points provide alow resolution grid which may be used for the coarse grain evaluation toidentify the active microtiles.

The processing unit may be configured to determine whether the polygonis located at least partially inside the selected smaller rectangulararea by: deriving a plurality of edges from the polygon; and comparingeach of the plurality of edges with a sample point associated with theselected smaller rectangular area to determine whether the selectedsmaller rectangular area is located wholly outside any of the edges;wherein if the selected smaller rectangular area is not located whollyoutside any of the edges then the polygon is determined to be located atleast partially inside the selected smaller rectangular area.

The processing unit may be configured to compare each of the pluralityof edges by: processing each of the plurality of edges to derive aplurality of processed edges, wherein the processing comprises, for eachedge, determining an orientation of the respective edge and applying atranslation to the respective edge in accordance with the orientation;comparing each of the plurality of processed edges with the samplepoint.

The processing unit may be configured to apply the translation to therespective edge in accordance with the orientation by: applying atranslation to the respective edge in one dimension, applying atranslation to the respective edge in two dimensions, or applying notranslation to the respective edge.

Each processed edge may be represented by a respective edge equation andthe processing unit is configured to compare each of the plurality ofprocessed edges with the sample point by evaluating the respective edgeequation at the sample point and determining whether the evaluationexceeds a predetermined threshold.

The processing unit may be configured to use the determination ofwhether the evaluation exceeds a predetermined threshold to determinewhether the sample point is located inside or outside the processededge.

In one example, if the processed edge equation evaluated at the samplepoint is positive, the smaller rectangular area with which that samplepoint is associated is identified as falling inside the edge from whichthe processed edge was derived and, if the processed edge equationevaluated at the sample point is negative, the smaller rectangular areawith which that sample point is associated is identified as fallingoutside the edge from which the processed edge was derived.

In one example, if the sample point is located inside the processededge, then the smaller rectangular area, with which the sample point isassociated, is located at least partially inside the edge from which theprocessed edge was derived, and if the sample point is located outsidethe processed edge, then the smaller rectangular area, with which thesample point is associated, is located wholly outside the edge fromwhich the processed edge was derived.

Each edge equation may be of the form E(x,y)=Ax+By+C, where A, B and Care constants specific to the processed edge, and the processing unitmay be configured to determine whether the evaluation exceeds apredetermined threshold by comparing −Ax with By+C. The processing unitmay be configured to output a first value if By+C>−Ax and output asecond value if By+C<−Ax, one of the first value and the second valueindicating that the sample point is located inside the processed edgeand the other of the first value and the second value indicating thatthe sample point is located outside the processed edge.

The graphics system may comprise a plurality of comparators forcomparing −Ax with By+C for each processed edge for all sample points ina rectangular area, each comparator associated with one sample point andone smaller rectangular area in the rectangular area.

Comparing −Ax with By+C for the processed edge may comprise reducing theprecision of “By+C” and comparing “−Ax” with the reduced precision“By+C”. This reduces the cost of the comparison.

In a first example, the processing unit is configured to determine, foreach polygon in the tiled set, whether that polygon is located at leastpartially inside a selected one of the smaller rectangular areas in theselected rectangular area, for all smaller rectangular areas in therectangular area in parallel for each edge of the polygon. Thecomparisons for all the polygon edges may be performed sequentially orin parallel.

In a second example, the processing unit is configured to determine, foreach polygon in the tiled set, whether that polygon is located at leastpartially inside a selected one of the smaller rectangular areas in theselected rectangular area, in a plurality of serial steps, each serialstep comprising identifying the smaller rectangular areas, of a subsetof the smaller rectangular areas in the rectangular area, falling atleast partially inside the polygon. The comparisons for all the polygonedges may be performed sequentially or in parallel.

In one example, each rectangular area is sub-divided into a plurality ofintermediate rectangular areas, each intermediate rectangular areacomprising a plurality of the smaller rectangular areas, and theprocessing unit is configured to determine, for each polygon in thetiled set, whether that polygon is located at least partially inside theselected one of the smaller rectangular areas by: determining whetherthat polygon is located at least partially inside a selected one of theintermediate rectangular areas in the selected rectangular area, theselected intermediate rectangular area including the selected smallerrectangular area; and if so, determining whether that polygon is locatedat least partially inside the selected one of the smaller rectangularareas, or if not, determining that that polygon is not located at leastpartially inside the selected smaller rectangular area.

That is, an additional level of hierarchy may be used to first divideeach rectangular area (tile) into intermediate rectangular areas(“minitiles”). Separate hardware units may be provided for eachhierarchical level or the evaluation at the different hierarchicallevels may make use of the same hardware unit.

In one example, the graphics system further comprises a rasterizing unitfor rasterizing those pixels in the selected smaller rectangular areathat are determined to be inside the polygon.

According to a third aspect, there is provided a graphics processingunit configured to render to a rendering space divided into a pluralityof rectangular areas, each rectangular area being sub-divided into aplurality of smaller rectangular areas each comprising a plurality ofpixels, the graphics processing unit comprising: an interface to amemory device; a microtiling unit arranged to receive via the interfacedata representing a tiled set of polygons to be rendered in a selectedone of the rectangular areas, determine for each smaller rectangulararea in the selected rectangular area whether that smaller rectangulararea contains at least a portion of a selected polygon, and output acorresponding indication; and a scan converter configured to receive theindications, and if a selected one of the smaller rectangular areascontains at least a portion of the selected polygon, determine which ofthe plurality of pixels in the respective smaller rectangular area areinside the selected polygon, and if a selected one of the smallerrectangular areas does not contain at least a portion of the selectedpolygon, perform no further processing of the selected polygon at one ormore of the plurality of pixels in the respective smaller rectangulararea.

The graphics processing unit may further comprise: a tiling unitconfigured to receive a plurality of image polygons to be rendered inthe rendering space, tile the image polygons to generate the tiled setof polygons by determining at least those image polygons that arelocated at least partially within the selected rectangular area, andoutput the tiled set of polygons to the memory device.

The microtiling unit may comprise edge calculation logic configured toreceive the selected polygon and derive a plurality of edge equationparameters for each edge of the selected polygon.

The microtiling unit may further comprise edge processing logic coupledto the edge calculation logic and configured to: receive the pluralityof edge equation parameters for a selected edge of the selected polygon;determine an orientation of the selected edge and apply a translation tothe edge equation parameters in accordance with the orientation togenerate processed edge equation parameters, wherein the translationcorresponds to a shift of the selected edge in one dimension, twodimensions, or no shift of the selected edge; and output the processededge equation parameters.

The edge processing logic may comprise a quadrant determination unitarranged to determine the orientation of the selected edge of thepolygon by evaluating the signs of one or more of the edge equationparameters.

The microtiling unit may comprise: a comparison unit configured toreceive the processed edge equation parameters and evaluate theprocessed edge equation parameters for each smaller rectangular area todetermine which of the smaller rectangular areas are located whollyoutside the selected edge of the polygon, and which are located at leastpartially inside the selected edge of the polygon.

The comparison unit may be further configured to: perform thedetermination of which of the smaller rectangular areas are locatedwholly outside the selected edge of the polygon, and which are locatedat least partially inside the selected edge of the polygon for each edgeof the selected polygon; and generate the indication such that any ofthe smaller rectangular areas that are not located wholly outside atleast one edge of the selected polygon are indicated as containing atleast a portion of a selected polygon.

The comparison unit may comprise: one or more evaluation unitsconfigured to receive the processed edge equation parameters andgenerate a first value from the processed edge equation parameters foreach of the smaller rectangular areas in dependence on its position inthe rectangular area, and a second value from the processed edgeequation parameters for each of the smaller rectangular areas independence on its position in the rectangular area.

The comparison unit may further comprise: a clamping unit configured toreceive the first value and generate a reduced first value by reducingthe precision of the first value in dependence on the number of bitsused to represent the second value.

The comparison unit may further comprise: a comparator array comprisinga plurality of comparators each associated with at least one of thesmaller rectangular areas and configured to operate in parallel, eachcomparator configured to compare the first value or the reduced firstvalue with the second value for its respective smaller rectangular areato determine whether that smaller rectangular area is located whollyoutside the selected edge of the polygon or located at least partiallyinside the selected edge of the polygon.

According to a fourth aspect, there is provided an apparatus forrendering in a graphics system having a rendering space divided into aplurality of rectangular areas and having each rectangular areasub-divided into a plurality of smaller rectangular areas eachcomprising a plurality of pixels, the apparatus comprising: means forreceiving data representing a tiled set of polygons to be rendered in aselected one of the rectangular areas; and means for determining, foreach polygon in the tiled set, whether that polygon is located at leastpartially inside a selected one of the smaller rectangular areas in theselected rectangular area; wherein the apparatus is arranged, if thatpolygon is located at least partially inside the selected smallerrectangular area, to determine which of the plurality of pixels in theselected smaller rectangular area are inside the polygon, and if thatpolygon is not located at least partially inside the selected smallerrectangular area, to perform no further processing of the polygon at oneor more of the plurality of pixels in the smaller rectangular area.

According to another aspect, there is further provided a computerreadable storage medium having encoded thereon computer readable programcode for generating the graphics processing unit of the third aspect.

According to another aspect, there is further provided a computerreadable storage medium having encoded thereon computer readable programcode for generating a processing unit configured to perform the methodof the first aspect.

Features described herein in relation to the method may also beapplicable to the system or apparatus, and features described inrelation to the system or apparatus may also be applicable to themethod.

BRIEF DESCRIPTION OF THE DRAWINGS

Examples will now be described in detail with reference to theaccompanying drawings in which:

FIG. 1 shows a prior art arrangement of a parallel row sampling approachwith a small triangle;

FIG. 2 shows a prior art system that is performing 4× anti-aliasing ofimage data;

FIG. 3 shows the triangle of FIG. 1 against the microtiles of anexample;

FIG. 4 shows a larger triangle against the microtiles of an example;

FIG. 5 shows classifications of edge orientation versus edge translationfor coarse grain evaluation;

FIG. 6 shows a first example for determining which microtiles are insidea given edge, using an array of compare units;

FIG. 7 shows a prior art example of a renderable image region surroundedby a guardband region used to reduce clipping costs;

FIG. 8 shows an example of a clamping unit used to reduce each highprecision By+C′ expression to a smaller number of bits, in order toreduce the cost of subsequent comparators;

FIG. 9 shows a second example for determining which microtiles areinside a given edge, using an array of compare units and incorporating aclamping unit like that in FIG. 8;

FIG. 10 shows full and iterative evaluation of intersected microtileswithin a tile;

FIGS. 11 a), b), c), d) and e) show an example which adds an additionallevel of hierarchy to the coarse grain evaluation;

FIG. 12 shows how the microtiling calculations should be adjusted toinclude the application of multi sample anti-aliasing (MSAA) to themicrotiling system;

FIG. 13 shows how all sample positions may be calculated from the topleft microtile when there is no multi sample anti-aliasing (non-MSAA);

FIG. 14 shows how all sample positions may be calculated from the topleft microtile when there is 4× multi sample anti-aliasing (4× MSAA);

FIG. 15 shows how all sample positions may be calculated from the topleft microtile when there is 2× multi sample anti-aliasing (2× MSAA);

FIG. 16 shows a flowchart of a method for reducing processing usingmicrotiles;

FIG. 17 shows a flowchart of a method for determining whether a polygonis located at least partially inside a microtile; and

FIG. 18 shows a block diagram of an example graphics processing systemfor implementing the method.

DETAILED DESCRIPTION

In recent years, as computer graphics models have become more complex,there has generally been a reduction in the average size of triangles.FIG. 1 shows an example of a prior art sampling approach used with asmall triangle 101. Referring to FIG. 1, assume that a typical, onscreen triangle is of the order of 18 pixels in area, so the width andheight are each approximately 6 pixels. If an example renderer isworking in parallel on row sets 103 of 16 pixels, (even if it isrestricted to only considering those row sets that intersect thetriangle, of which there are seven (shown shaded, 105) in FIG. 1), thenonly approximately 16% of the pixels in each row set 105 will be foundto be inside the triangle. This low level of utilisation (the proportionof processed pixels that a triangle intersects) is undesirable.

Aliasing is a well-known problem in computer graphics which stems fromsampling a signal at below the Nyquist limit. This is often apparentwhen only one sample point is taken per pixel. Pragmatic solutions, suchas supersampling or multisampling, which involve taking several samplesper pixel, and subsequently filtering, are often used in the art. Thismay be considered equivalent to initially rendering at a higher pixelresolution. It should be noted, therefore, that in this specification,the term “sample” and the term “pixel” may be used interchangeably. FIG.2 shows a prior art system that is performing 4× anti-aliasing of imagedata, in which a 3*4 subset 201 of the image pixels is shown. “Within”each pixel are defined four sampling locations 203: the same pattern oflocations is used in each pixel. This means that there are sets of“related” sample locations 205 separated, in the x- and y-directions byregular 1 pixel widths/heights. This can further exacerbate the lowlevel of utilisation.

One way to counteract the low utilisation is to reduce the tile size.However, there is a trade-off associated with the tiling/binning processand the chosen tile size. Smaller tiles (or at least smaller granularityin the binning process), typically result in more efficient renderingdue to a higher ratio of pixels being covered by each tested primitive.However, for a given image dimension, smaller tiles imply a largernumber of tiles and hence a greater number of object lists that need tobe stored and managed.

The method and apparatus described herein provides a technique forincreasing the utilisation without incurring the storage and managementcosts of reducing the tile size. As described below, this techniquedivides each rectangular area (tile) into smaller rectangular areas(microtiles). The technique first identifies which smaller rectangularareas (microtiles) are intersected by a polygon (i.e. fall at leastpartially inside the polygon), and then only processes those identifiedsmaller rectangular areas. Thus, the identified smaller rectangularareas are the active microtiles. By performing the initialidentification at microtile scale, which is a relatively coarse grainevaluation, subsequent processing costs can be reduced. Throughout thisspecification, the term “rectangular area” is used interchangeably withthe term “tile”, the term “smaller rectangular area” is usedinterchangeably with the term “microtile” and the term “primitive” isused interchangeably with the term “polygon”. Note that the term“rectangular” is intended to encompass square.

FIG. 3 shows the triangle 101 of FIG. 1 against 20 4*4 pixel microtiles303. The microtiles which are intersected by triangle 101 (the activemicrotiles 305) are shown shaded in FIG. 3. The utilisation level forthe FIG. 1 example rendering method, was only approximately 16%, asnoted above. However, using the method described herein, the utilisationlevel (the proportion of pixels within active microtiles 305 whichtriangle 101 intersects) would, typically, nearly double, toapproximately 30%.

FIG. 4 shows a larger triangle 401 in a 32*32 pixel tile 403 including64 4*4 microtiles 405. The intersected microtiles 407 are shaded in FIG.4. In this example, sample points 409 are provided at the top left handcorner of each microtile. Only those microtiles which are active areprocessed for the triangle shown in FIG. 4, and no further processing isrequired for the other microtiles. Thus, microtiles that intersect thetriangular polygon are first identified and then those which areintersected are processed. As a result of this, the following can beachieved:

-   -   Relatively inexpensive low precision calculations can be used to        initially identify active microtiles (microtiles that fall at        least partially within a polygon).    -   Small polygons can be dealt with efficiently within a        proportionately large tile. In a tile-based renderer, being able        to use larger tiles reduces the cost of the tiling/binning        process.    -   Polygons with extreme aspect ratios, such as line polygons, can        be dealt with efficiently.    -   It is possible to extend the method and system to handle multi        sample anti-aliasing on all edges.    -   There is a reduction in the number of wasted calculations        relative to non-square processing footprints.    -   Microtiles can be processed in any order thereby allowing        implementation of load balancing schemes in subsequent        processing.    -   Flexibility is provided in being able to process microtiles        independently of an associated polygon.

The method and apparatus, which leads to the above features, will now bedescribed.

FIG. 16 illustrates a flowchart of an overall method for reducingprocessing and increasing the utilisation level using microtiles. Instep 1602 a set of polygons are received in connection with a selectedone of the tiles (rectangular area). This set of polygons representsthose polygons of an image that have been determined to be present inthe selected tile. Therefore, the set of polygons corresponds to theobject list for the tile, as generated by the tiling/binning process,and is referred to as a tiled set of polygons. The tiled set of polygonsmay be in the form of a list of references to parameters of thepolygons, or may contain the polygon parameters.

Each polygon in the tiled set is then evaluated in connection with eachmicrotile (smaller rectangular area) as shown in step 1604. For example,a polygon is selected from the tiled set, and then evaluated inconnection with a selected microtile. This can be repeated for eachmicrotile, and then another polygon selected and the overall processrepeated. In alternative examples, this can be reversed, such that amicrotile is selected, and then each polygon evaluated for thatmicrotile before selecting another microtile.

For a selected polygon and a selected microtile, in step 1604 it isdetermined whether the selected polygon is located at least partiallyinside (i.e. not wholly outside) the selected microtile. If, in step1606, the selected polygon is found to be located at least partiallyinside the selected microtile, then in step 1608 an indication isgenerated that further processing of that polygon should be performed inthe microtile. In other words, because it has been determined that thepolygon is present in that microtile, then additional renderingoperations should continue to be performed for that polygon in thatmicrotile. This includes scan conversion operations to determine whichof the pixels in that microtile are inside the polygon, and may furtherinclude, for example, depth testing, or any other rasterisationfunctions.

Conversely, if in step 1606 the selected polygon is found to be locatedwholly outside the selected microtile, then in step 1610 it is indicatedthat further processing of the polygon can be skipped in that microtile.In other words, because the polygon is not present within the microtile,then the pixels within that microtile will not be covered by thepolygon. This means that additional rendering operations in connectionwith the polygon can be avoided for the pixels in that microtile, asthat polygon will have no influence upon them.

Reference is now made to FIG. 17, which illustrates a more detailedflowchart of an example process for determining whether a polygon islocated at least partially inside a microtile (i.e. a more detailedflowchart of operations performed by step 1604). In step 1702, edgeequation parameters are derived for each edge of the selected polygon.Example edge equations are discussed in more detail below. Then, foreach edge, a determination is made in step 1704 whether a sample pointassociated with the microtile is inside or outside the edge. Once aninside/outside result is known for all edges of the polygon, then thesecan be combined in step 1706 to determine whether the overall polygon iseither partially inside or wholly outside the microtile.

FIG. 17 also shows an example process for determining whether a samplepoint associated with the microtile is inside or outside the edge instep 1704. An orientation for the edge is determined in step 1708, asdescribed in detail below, and a corresponding translation applied tothe edge equation parameters in dependence on the orientation. Thistranslation enables the result obtained for the sample point of themicrotile to apply to the microtile as a whole. First and second valuesare then generated in step 1710 using the translated edge equationparameters and the location of the sample point of the microtile withinthe tile. The first and second values are compared in step 1712 toprovide the determination of whether the sample point is inside oroutside the edge. Details on the generation of the first and secondvalues and their comparison are provided below.

FIG. 18 illustrates a block diagram of an example graphics processingsystem for implementing the above-described method. The graphicsprocessing system receives polygons 1802 for an image, and a tiling unit1804 processes these polygons to perform tiling/binning, and determinewhich polygons are within which tiles. The outputs of the tiling unit1804 are tiled polygon sets (object lists) for each tile. These areoutput to a memory device 1806.

A microtiling unit 1808 is arranged to perform the operations describedin FIGS. 16 and 17 above. The microtiling unit 1808 receives the tiledpolygon set for a given tile from the memory device 1806 via aninterface 1810. A selected polygon from the tiled polygon set isprovided to edge calculation logic 1812, which derives the edge equationparameters for each edge. Edge processing logic 1814 is coupled to theedge calculation logic 1812 and receives the edge equation parameters.The edge processing logic 1814 determines the orientation of each edgeand applies the appropriate translation. The edge processing logic 1814may comprise quadrant determination logic 1816 for determining the edgeorientation. The processed edge equation parameters for the polygon areprovided to a comparison unit 1818 coupled to the edge processing logic1814. The comparison unit 1818 determines whether the selected polygonis either partially inside or wholly outside each microtile in the giventile. The comparison unit 1818 comprises one or more evaluation units1820 that receive the processed edge equation parameters and calculatethe first and second values based on the processed edge equationparameters and the location of each sample point in each the microtile.One or more comparator arrays 1822 are arranged to receive the first andsecond values, and compare them to determine whether the selectedpolygon is either partially inside or wholly outside each microtile.This result can be output from the comparison unit 1818 in the form ofan indication of which microtiles should be subject to furtherprocessing in connection with the selected polygon, and provided to ascan converter 1824, for example.

In one example, the evaluation units 1820 can be structured to performoperations in parallel, for example calculating the first and secondvalues in parallel and/or calculating values for multiple edges inparallel (e.g. three edges if the polygon is a triangle). In alternativeexamples, there may be fewer evaluation units 1820, e.g. one thatserially calculates the first and second values for each edge.Similarly, the comparator arrays 1822 can also be structured to operatein a parallel manner in one example. For example, there can be onecomparator for each microtile in the comparator array 1822, and thecomparators operate in parallel to perform the comparison for eachmicrotile concurrently. In an alternative example, one comparator canperform the comparison for a plurality of microtiles, taking each inturn (e.g. one comparator for each row or column of microtiles). Inaddition or alternatively, there can be a comparator array for each edgeto enable all edges of the polygon to be compared in parallel (e.g.three comparator arrays if the polygon is a triangle).

More detail on the above elements is now provided below.

Polygon Edge Equations

Polygons used in graphic systems are typically triangles. When thesereach the rendering stage of a graphics system they can be defined bythree edge equations and a depth equation. The examples described hereevaluate each edge equation at all points on a fixed grid of samplepositions. In an example, the edge equations are each of the formE(x,y)=Ax+By+C, where x and y represent either a screen location, apixel location or, in the case of supersample anti-aliasing, a subpixellocation.

A, B and C may be pre-calculated fixed point precision constantcoefficients specific to the polygon edge. A, B, and C are usuallygenerated from triangle vertex coordinates that themselves (for reasonsof guaranteeing mathematical stability) are represented by fixed-pointcoordinates of bounded range. Thus, the number of bits in eachcoefficient can be known precisely.

To reduce the cost of evaluation within a tile, C may be pre-adjustedsuch that the scene origin is translated to the sample location of thetop-left pixel in the tile. This makes processing more efficient becauseit reduces the range and magnitude of the x and y values which, in turn,reduces the size of the mathematical operations needed to evaluate theedge equations. Such a translation can be performed directly on thevertex coordinates, prior to computation of each edge's A, B and Ccoefficients, or applied to the C value after the calculations on theoriginal coordinates.

The primitive edges can be considered to be vectors and have a direction(e.g.

clockwise) around the primitive. Thus, in this clockwise example, if alocation is to the right of the edge, it can be considered to be insidethe edge, but if a location is to the left of the edge, it can beconsidered to be outside the edge. Therefore, if the edge vectors aredirected in a clockwise fashion around the polygon, given any x and yvalues within the tile being processed, if E(x,y) is positive (greaterthan zero), then the sample point (x,y) is inside the edge beingevaluated; if E(x,y) is negative (less than zero), then the sample point(x,y) is outside the edge being evaluated; and if E(x,y) is zero, thenthe sample point lies precisely on the edge E. For detailedrasterization, the case where E(x,y) is zero must be handled by a tiebreaking rule (for example, the OpenGL “fill rule”). The coarse grainevaluation (i.e. the initial identification of which microtiles fall atleast partially inside the polygon), however, may instead opt to use aconservative, slightly cheaper alternative of assuming that the samplepoint is inside the edge. In order for a sample point to lie within apolygon, it must be inside all of the edges.

The above description applies, directly, to the per-pixel (orper-subpixel) inside tests required for subsequent detailedrasterization. However, in one example, in order to perform the coarsegrain evaluation (i.e. the initial identification of which microtilesfall at least partially inside the polygon), each edge equation, E(x,y),must be adjusted. In summary, if any sample location in the microtile isinside the edge, then the corresponding sample point must also indicate“inside” when evaluated against the adjusted edge equation. Conversely,if the sample point indicates “outside” then all sample locations in themicrotile must be outside the edge. The adjustment is equivalent totranslating the edge. More specifically, the C coefficient of eachequation is adjusted to give C′ according to the orientation of theedge. The orientation, in turn, is specified by the edge's A and Bcoefficients. A summary of this process is given below.

Edge Translations

As discussed above, in order to perform inside tests that apply to amicrotile of pixels using this coarse grain evaluation (i.e. the initialidentification of which areas fall at least partially inside thepolygon), each edge equation E(x,y), should be adjusted to becomeE′(x,y). Each primitive edge may need to be translated, depending onorientation, by the width and/or height of the microtile.

FIG. 5 shows translation operations for various polygon edgeorientations for the initial identification of which microtiles fall atleast partially inside the polygon, for the illustrative example of whenthe microtile sample point for each microtile is at the top left cornerof the microtile. The chosen microtile size may be such that thetranslation of each edge is inexpensive. In the example illustrated inFIG. 5, eight illustrative 4*4 sample microtiles 501 are shown eachintersecting with a respective edge 503. The orientation of each edge503 is such that it only glances the microtile 501. Actual fixed samplepoints (solid circles 505) are shown at the top left corner of eachmicrotile, and ideal sample points (empty circles 507) are also shown.The ideal sample points are the points that enable a determination ofwhether the microtile as a whole is inside or outside the particularedge. The ideal sample point changes depending on the orientation of theedge as shown in FIG. 5. The relative positions of the actual samplepoint 505 and the ideal sample point 507 determine the appropriatetranslation of an edge. The translated edges are shown in dotted linesat 509. In the example illustrated in FIG. 5, where a 4*4 samplemicrotile is employed, the translation in the x and y directions, t_(x)and t_(y), will each be either 0 or 4 samples. Adjustment of coefficientC to give C′ is then simply a matter of subtracting 4A or 4B or both, orleaving C unchanged.

As shown in FIG. 5, the decision whether to translate the edge vector,and in which direction, is dependent on its slope or orientation. Thisis easily determined from the signs of the A and B coefficients:

Quadrant 0: B negative, A positive.

Quadrant 1: B positive, A positive.

Quadrant 2: B positive, A negative.

Quadrant 3: B negative, A negative.

The required edge translations therefore become:

Quadrant 0: C′=C−(A.t_(x)+B.t_(y))=translation up and left.

Quadrant 1: C′=C−A.t_(x) =translation up.

Quadrant 2: C′=C=no translation.

Quadrant 3: C′=C−B.t_(y)=translation left.

The evaluation of each sample point on the coarse microtile grid onlyhas to return the sign bit of the processed edge equation with theappropriate translation applied E′(x,y) and not the actual value. Theoutcome of the evaluation is then a Boolean indicating whether any partof the microtile is inside the processed edge E′(x,y).

The processed edge E′(x,y)=Ax+By+C′, so it can be seen that

-   -   By+C′≧−Ax is: TRUE for E′(x,y)≧0    -   and FALSE for E(x,y)<0.

Thus, if By+C′≧−Ax is TRUE, the sample point (x,y) is inside the edgebeing evaluated or precisely on the edge being evaluated (which can betreated as inside the edge in this coarse grain evaluation); and ifBy+C′−Ax is FALSE, the sample point (x,y) is outside the edge beingevaluated. In this example, such a magnitude comparison is used, sincethis is less costly than an extra add and a compare against zero thatwould be required if E′(x,y) were fully evaluated.

By selecting a microtile size that is a power of two in sample width andheight, the full coarse sample grid for the tile becomes simple tocalculate. For example on a 32*32 sample tile with 4*4 sample microtilesthe Ax terms are:

0, −4A, −8A, −12A, −16A, −20A, −24A, −28A (x=0 . . . 28 in increments of4). Calculation of these eight values and their negation iscomputationally inexpensive. Similarly the eight By+C′ terms are alsoinexpensive:

C′, 4B+C′, 8B+C′, 12B+C′, 16B+C′, 20B+C′, 24B+C′, 28B+C′ (y=0 . . . 28in increments of 4).

It will be appreciated that common terms can be shared, whereappropriate, amongst these evaluations.

Comparators

FIG. 6 shows a first example for determining which microtiles are insidea given edge, using a comparison of By+C′ and −Ax. Given Nx*Nymicrotiles in a tile, the set of Nx, −Ax terms, and the set of Ny, By+C′terms can be computed by one or more evaluation units 1820 in

FIG. 18) and compared using an Nx*Ny grid of comparators (comparatorarray 1822 from FIG. 18). FIG. 6 illustrates this arrangement for anexample with a 32*32 sample tile 601 and 4*4 sample microtiles 603. Theexample of FIG. 6 therefore requires a grid of 8*8 comparators 605 toundertake the coarse grain evaluation for an edge on all microtiles inparallel. Note that virtually the same scheme can be used for the insidetests for the rasterization step.

To support triangular polygons, a one example would have three suchunits, one for each of the three triangle edges. An alternative examplemight reuse a smaller number of units over several clock cycles. Anexample that supports wide line segments (i.e. parallelograms) may havefour of these units, and similarly for other many sided polygons.

Further Reducing the Cost for Comparisons

Although the above is relatively inexpensive, the cost of the coarsegrain evaluation may be further reduced.

As already noted, the input vertex coordinates of a polygon aregenerally represented by fixed-point values. These can be considered tobe expressed as a multiple of the pixel dimensions plus some number ofbits of sub-pixel precision. Therefore, each x or y position may berepresented by a J-bit number consisting of H integer bits and Kfractional bits. The positions can be represented in either signed orunsigned fixed point. For illustrative purposes, signed format will beassumed, but it will be appreciated that the techniques described couldeasily be adapted for a system using unsigned numbers.

In one example, J may be 16, with 12 integer and 4 fractional bits,allowing each x,y coordinate value to be anywhere in the range [−2048,2047.9375]. Such an example would be suitable for rendering images of,say, 2k*2k pixels with a significant “off-screen” guardband region. FIG.7 shows an example of a renderable image region surrounded by aguardband region used to reduce clipping costs. In FIG. 7, therenderable image region 701 is centred within the maximum range ofvertex positions 703 i.e. the image pixels span coordinates [−1024,1024]. The renderable image region 701 is surrounded by guardband region705. Also shown in FIG. 7 is a polygon 707 having an on-screen portion709 within the renderable image region 701 and an off-screen portion 711in the guardband region 705.

For an edge extending between point P (X_(P), Y_(P)) and the point Q(X_(Q), Y_(Q)), the A, B and C coefficients, expressed in screencoordinates, may be represented as:

A _(PQ) =Y _(P) −Y _(Q)

B _(PQ) =X _(Q) −X _(P)

C _(PQ) ^(SCREEN) =X _(P) Y _(Q) −X _(Q)Y_(P)

The A and B coefficients can each be exactly represented in J+1 bits.Although it may at first appear that the C coefficient will require 2J+1bits, analysis of the range of results possible from signed J-bitcoordinate values shows that 2J bits are sufficient. Allowing for themapping of C from screen coordinates to tile-based coordinates, weobtain:

C _(PQ) ^(TILE)=(X _(P) Y _(Q) −X _(Q) Y _(P))+A _(PQ) .i _(X) +B _(PQ).T _(Y)

where T_(X) and T_(Y) identify the corner of the tile.

This, in turn, may be shifted for the coarse grain evaluation to obtain:

C′ _(PQ)=(X _(P) Y _(Q) −X _(Q) Y _(P))+A _(PQ).(T _(X)−{0,1}.t _(x))+B_(PQ).(T _(Y)−{0,1}.t _(y))

Note that T_(X), T_(Y), t_(x) and t_(y) are expressed in the fixed pointrange. Note that this expression may require additional bits ofprecision, and this depends on the relative sizes of the maximumsupported image and the guardband sizes (see FIG. 7). It can be assumedthat C′_(PQ) requires L bits, where L≧2J.

Now consider the coarse grain evaluation expressions of the form

By+C′≧−Ax

as discussed in relation to the example of FIG. 6.

Each of the Ny, “B(4j)+C′” expressions uses L bits to accuratelyrepresent them. However, each of the Nx, “−A.4i” expressions requireconsiderably fewer bits to be accurately represented. In an example, theworst case (i.e. maximum number of required bits) is determined by −28A.This requires only M=J+1+3 bits. Note that the multiplier is a multipleof t_(x), which in examples is of the form 2^(T). Therefore, the T leastsignificant integer bits and the K fractional bits will all be zero. Inexamples, L is therefore significantly greater than M.

FIG. 8 shows an example of a clamping unit 800 to reduce the precisionof a single B(4j)+C′ value from L bits to M+1 bits, with the option of afurther 1 bit flag output. The L-bit input value 801, is separated intothree sets of contiguous bits: the T+K least significant bits (LSBs)803, the next M more significant bits 805, to produce output value 807,and then the remaining most significant bits (MSBs), 809.

For cases where it is necessary to detect the special case By+C′=−Ax(e.g. for examples in which a more conservative coarse grain evaluationis used, i.e. where a sample point falling precisely on the edge cannotsimply be considered as inside the edge), the least significant bits aretested at unit 811. Unit 811 tests to establish if any of the leastsignificant bits are non-zero, and a Boolean flag 813 is then generated.Unit 811 is thus a T+K input OR gate. For examples of the coarse grainevaluation in which By+C′−Ax is used to define “inside” the edge, units803 and 811 are not included.

The most significant bit of output value 807 is duplicated, 815, andconcatenated, 817, as the least significant bit, with the output of 809,to form an L−(M+T+K)+1-bit value, 819. The bits of value 819 are tested,at unit 821, to determine if the original value is outside the range ofvalues representable by M bits, i.e. either <−2^(M+1) or 2^(M−1), and toindicate this to a clamp unit, 823. The test performed by unit 821 andthe actions taken by clamp unit 823 are as follows:

-   -   a) When value 819 is not all 1's and the sign bit is set (i.e.        the original fixed-point input value is <−2 ^(M−1)), then a        value in the range [−2^(M), −2^(M−1)−1] is output.    -   b) When value 819 is not all 0's and the sign bit is not set        (i.e. the original fixed-point input value is ≧2^(M−1)), then a        value in the range [2^(M−1), 2^(M)−1] is output.    -   c) Otherwise (i.e. the original fixed point input value is in        the range [−2^(M−1), 2^(M−1)−1]), value 807 is sign extended to        M+1 bits and output at 825.

Thus, clamping unit 800 reduces the precision of a single B(4j)+C′ value801 from L bits to M+1 bits output at 825, and, optionally, a Booleanflag, 813.

In a first example, for case a) above, the value −2^(M) is output, whilefor case b) above, the value 2^(M−1) is output. A second exampleslightly reduces the hardware costs: for case a) a (non constant) M+1bit value is constructed with ‘10’ as the top (most significant) twobits followed by the less significant M−1 bits of value 807; for case b)a M+1 bit value is constructed with ‘01’ as the top (most significant)two bits followed, again, by the less significant M−1 bits of value 807.It will be appreciated that, for the output generated by clamp unit 823,the M−1 output bits are no longer a function of the test done by unit821. Only the top two MSBs are ever changed according to cases a), b)and c) above.

FIG. 9 shows a second example for determining which microtiles areinside a given edge, using a comparison of By+C′ and −Ax, butincorporating clamping units 800 like that in FIG. 8. FIG. 9 representsan improvement over the example of FIG. 6: by using the precisionreduction logic of FIG. 8, the costs of a coarse grain evaluation can bereduced. As in FIG. 6, FIG. 9 illustrates this arrangement for anexample with a 32*32 sample tile 601, 4*4 sample microtiles 603 and agrid of 8*8 comparators 605 to evaluate the inside test for an edge onall microtiles in parallel. FIG. 9 further includes clamping unit 900containing Ny copies of the clamping unit 800 of FIG. 8. This clampseach of the Ny B(4j)+C′ computed values to not exceed the maximum orminimum of an M+1 signed fixed-point number. By reducing the number ofbits in the numbers to be compared, the clamping operation reduces thecost (in terms of complexity, silicon area and/or power consumption) ofeach of the comparators in the array 605.

As identified earlier, for cases where the expression By+C′−Ax isinstead separated into By+C′>−Ax and By+C′=−Ax conditions, the Nycomponents of clamping unit 900 would each include units 803 and 811.The asserted 813 signal would then be tested in each of the comparators.As noted, the Ax values do not include the T+K LSBs because those bitvalues, in these examples, are implicitly zero. The presence of anasserted 813 signal, therefore, implies inequality.

An alternative example is able to make further savings taking advantageof the fact that the left half of the Nx “−A.4i”s are smaller still inmagnitude, and so an additional clamping operation may be performed.Diminishing returns are achieved with further applications of thisprocedure, however. In a further example, C′ is computed relative to thecentre of the tile rather than the corner, allowing a further smallreduction in the magnitudes of the various values.

Active Microtiles within a Tile—Full or Iterative Evaluation

FIG. 10 shows full and iterative evaluation of intersected microtileswithin a tile, for example using the array of comparators of FIG. 6 orFIG. 9. FIG. 10 is a modified version of FIG. 4. As in FIG. 4, FIG. 10shows a triangular primitive 401 in a 32*32 sample tile 403 including 644*4 microtiles 405. The microtiles 407 which are intersected byprimitive 401 are shaded in FIG. 10. Sample points 409 are provided atthe top left hand corner of each microtile.

In a first example (full evaluation), the example depicted in FIGS. 4and 10 accepts as inputs the A, B, and C coefficients for a set of edgesand evaluates, for each edge, the eight “−Ax” terms against the eight“By+C′” terms. All sample locations 409 are thus evaluated for all edgesin parallel. As noted earlier, for each edge, the entire 32*32 tile canbe microtiled in a single clock with 8×8 comparators and 8+8calculations (8 calculations to derive the 8 “−Ax” terms and 8calculations to derive the 8 “By+C” terms).

In an alternative example of full evaluation, where the A, B and C edgecoefficient sets arrive serially, a single design can be used toevaluate microtiles for each triangle edge in turn, in an subtractivemanner. Discounting microtiles outside one current edge equation can bedone for the entire tile in a single phase. At the end of the thirdedge, only the microtiles identified as contributing to the trianglewill remain. The resulting map of up to 64 active microtiles can then beprocessed for detailed triangle edge and pixel depth evaluation.

In a second example (iterative evaluation) also illustrated in FIG. 10,rather than evaluating all sample locations in parallel, the exampleiterates in the y-direction between the maximum and minimum y extent ofthe object at microtile granularity. For each iteration, a “By+C′” valueis calculated for the microtile row and eight “−Ax” values aregenerated. A row of microtiles can be evaluated with 8 comparators. Onesuch row, indicated by the black sampling locations, is shown at 1000.The previously evaluated rows are shown at 1002, and the rows yet to beevaluated are shown at 1004.

In the example of a 32*32 tile with 4*4 microtiles, a single edgeequation can be tested against the whole tile in a maximum of 8 clockswith each clock using 8+1 calculations (8 calculations to derive the 8“−Ax” terms and 1 calculation to derive the “By+C” term) and 8comparators. This is an inexpensive implementation which lends itself toreplication e.g. three replications each working on its own edgeequation in parallel. The output of each of the three evaluations arethen logically AND-ed (+) to yield the final coverage result for themicrotile row.

Identification of Active Minitiles

FIGS. 11 a), b), c), d) and e) depict a further example which adds anadditional level of hierarchy to the coarse grain evaluation. FIG. 11 a)is a modified version of FIG. 4. As in FIG. 4, FIG. 11 a) shows atriangular primitive 401 in a 32*32 sample tile 403. However, eachsample tile 403 is now divided into four intermediate rectangular areas(minitiles) 1101 b, 1101 c, 1101 d and 1101 e. Each minitile 1101 b,1101 c, 1101 d, 1101 e is 16*16 pixels. Each minitile comprises 16 4*4microtiles 405 (shown more clearly in FIGS. 11 b) to e)). Thus, as inFIG. 4, each 32*32 sample tile 403 includes 64 4*4 microtiles 405.

An additional level of hierarchy is provided in the coarse grainevaluation. Before the active microtiles are identified, the activeminitiles are identified. That is, the minitiles which are intersectedby triangular primitive 401 are first identified. This is done using thesame approach as already described in relation to microtiles, and samplepoints 1103 for each minitile 1101 b, 1101 c, 1101 d, 1101 e areprovided at the top left hand corner of each minitile. In this example,the edge translations used in the calculations will be of minitile (halftile) x- and y-magnitude rather than microtile magnitude for the foursample points 1103. In this example, this is done using four “−Ax”calculations, four “−By+C” calculations and 4*4 comparators in a maximumof four phases.

In this example, three minitiles 1101 b, c, and d, are active minitiles.Primitive 401 does not intersect minitile 1101 e, which is therefore notactive. Then, for each active minitile in turn, active microtiles withinthat minitile are identified, as already described, and this is shown in

FIGS. 11 b) to d). Sample points 409 for identification of the activemicrotiles (in each minitile) are provided at the top left corner ofeach microtile.

FIG. 11 b) shows the triangle 401 against the first active minitile 1101b. This is the minitile at the top left of tile 403. The microtiles 1105b in minitile 1101 b which are intersected by the primitive 401 (theactive microtiles) are shaded in FIG. 11 b).

FIG. 11 c) shows the triangle 401 against the second active minitile1101 c. This is the minitile at the top right of tile 403. Themicrotiles 1105 c in minitile 1101 c which are intersected by theprimitive 401 (the active microtiles) are shaded in FIG. 11 c).

FIG. 11 d) shows the triangle 401 against the third active minitile 1101d. This is the minitile at the bottom right of tile 403. The microtiles1105 d in minitile 1101 d which are intersected by the primitive 401(the active microtiles) are shaded in FIG. 11 d).

FIG. 11 e) shows the triangle 401 against the inactive minitile 1101 e.This is the minitile at the bottom left of tile 403. There are no activemicrotiles in minitile 1101 e. There is no need to perform microtilecalculations for a minitile that has been identified as inactive.

By identifying the active minitiles before identifying the activemicrotiles (i.e. by introducing an additional level of hierarchy intothe coarse grain evaluation), efficiency can be improved even further.

Super-Sampling and Multi-Sample Anti-Aliasing

In a system that supports various modes of super-sampling anti-aliasing(SSAA) or multi-sample anti-aliasing (MSAA), the microtilingcalculations can be adjusted to suit the number of pixels between eachpoint on the coarse sampling grid. FIG. 12 and Table 1 show the distancebetween microtile sample points for a system using a 4*4 samplemicrotile, for non-MSAA, 2× MSAA and 4× MSAA. In FIG. 12 and Table 1, 2×MSAA is horizontal sub-sample stacking i.e. additional resolution in thehorizontal direction. 4× MSAA is additional resolution in both thehorizontal and vertical directions. The principle readily extends to anysize of microtile, but powers of two samples will be more efficient toimplement.

TABLE 1 Non-MSAA 2xMSAA 4xMSAA Horizontal spacing 4 samples = 4 samples= 4 samples = 4 pixels = 4A 2 pixels = 2A 2 pixels = 2A Vertical spacing4 samples = 4 samples = 4 samples = 4 pixels = 4B 4 pixels = 4B 2 pixels= 2B

Note in FIG. 12 that microtile sample point positions are separated by xand y integers. The anti-aliasing mode employed only affects thedistance between sample points. Any sub-pixel grid offsets that need tobe employed in fine grain pixel evaluations, such as the offsets shownin FIG. 2, do not need to be accounted for in the coarse grainevaluation (microtiling) phase.

Detailed Rasterization and Depth Processing

Identification of active microtiles in the coarse grain evaluation stillleaves the processing of microtiles at pixel or sub-pixel resolution tobe performed. The scan conversion of each microtile and the depthprocessing for each active pixel may be implemented with calculationsthat can be optimised given the presence of microtiles. Each triangularprimitive may be defined by three edge equations (already discussed indetail) and a depth equation which allows depth processing to beperformed, and each pixel to be shaded according to which primitives arevisible in that pixel. By calculating the depth and edge equation termsfor the top left sample point within a microtile and using this as a“base value”, the remaining sample points (there are 15 remaining samplepoints in an exemplary 4*4 microtile) can be found with integer additionof A and B coefficients. An exemplary method is described below withreference to FIGS. 13, 14 and 15 for various sampling modes. Thefollowing equations incorporate sub-pixel grid offsets, dx and dy, whichreflect the position of a sampling point within a pixel. For microtileevaluation, where the sampling point was at the top left corner of themicrotile, no such offset was required. For edge processing a similartechnique to that used in microtile evaluation may be employed, where“−A.(x+dx)” and “B.(y+dy)+C′” terms are compared. For the depthcalculation the actual depth value of z(x,y)=A.(x+dx)+B.(y+dy)+C must befound.

FIG. 13 shows how all sample positions may be calculated from the topleft microtile 1301 when there is no multi sample anti-aliasing(non-MSAA, Table 1, left hand column). The top left sample position iscalculated. From this value, the top left 4 pixels can be found byadding A and/or B. The remaining 12 sample positions can be found fromthose top left 4 pixels by addition of a further 2A and/or 2B. Notethat, although they are not illustrated, the initial Ax and By terms mayinclude any sample grid offsets, dx, and dy.

FIG. 14 shows how all sample positions may be calculated from the topleft microtile 1401 when there is 4× multi sample anti-aliasing (4×MSAA, Table 1, right hand column). Four samples in the top left of themicrotile are calculated at their site-specific sample grid offsetdx_(n), dy, where n=0 . . . 3. The remaining 12 samples can be foundwith the addition of A and/or B only.

FIG. 15 shows how all sample positions may be calculated from the topleft microtile 1501 when there is 2× multi sample anti-aliasing (2×MSAA, Table 1, middle column). In the example shown in FIG. 15, andaccording to Table 1, there is increased resolution in the x-dimension(horizontal sub-sample stacking) requiring only +A to be added whentraversing in the x-direction. The y-dimension requires a unit additionof B between any two contiguous samples vertically. It is, of course,equally valid to choose a scheme where the resolutions in the x- andy-directions are transposed, such that vertical sub-sample stacking isachieved. This would require A to be added between any two horizontallyadjacent samples and B to be added at half the rate vertically. Thechoice of implementation of horizontal or vertical sub-sample stackingdoes not affect the principle behind the microtiling algorithm oradversely affect the cost of implementation.

We claim:
 1. A method of rendering in a graphics system having arendering space divided into a plurality of rectangular areas and havingeach rectangular area sub-divided into a plurality of smallerrectangular areas each comprising a plurality of pixels, the methodcomprising: receiving data representing a tiled set of polygons to berendered in a selected one of the rectangular areas; for each polygon inthe tiled set, determining whether that polygon is located at leastpartially inside a selected one of the smaller rectangular areas in theselected rectangular area; and if that polygon is located at leastpartially inside the selected smaller rectangular area, determiningwhich of the plurality of pixels in the selected smaller rectangulararea are inside the polygon, or if that polygon is not located at leastpartially inside the selected smaller rectangular area, performing nofurther processing of the polygon at one or more of the plurality ofpixels in the smaller rectangular area; and wherein the step ofdetermining whether the polygon is located at least partially inside theselected smaller rectangular area comprises: deriving a plurality ofedges from the polygon data; and comparing each of the plurality ofedges with a sample point associated with the selected smallerrectangular area to determine whether the selected smaller rectangulararea is located wholly outside any of the edges; wherein if the selectedsmaller rectangular area is not located wholly outside any of the edgesthen the polygon is determined to be located at least partially insidethe selected smaller rectangular area.
 2. A method according to claim 1,further comprising: receiving a plurality of image polygons to berendered in the rendering space; and tiling the image polygons togenerate the tiled set of polygons by determining at least those imagepolygons that are located within the selected rectangular area.
 3. Amethod according to claim 1, wherein comparing each of the plurality ofedges comprises: processing each of the plurality of edges to derive aplurality of processed edges, wherein the processing comprises, for eachedge, determining an orientation of the respective edge and applying atranslation to the respective edge in accordance with the orientation;and comparing each of the plurality of processed edges with the samplepoint.
 4. A method according to claim 3, wherein applying thetranslation to the respective edge in accordance with the orientationcomprises: applying a translation to the respective edge in onedimension, applying a translation to the respective edge in twodimensions, or applying no translation to the respective edge. 5.(canceled)
 6. A method according to claim 5, further comprising usingthe determination of whether the evaluation exceeds a predeterminedthreshold to determine whether the sample point is located inside oroutside the processed edge.
 7. A method according to claim 6, wherein ifthe sample point is located inside the processed edge, then the smallerrectangular area, with which the sample point is associated, is locatedat least partially inside the edge from which the processed edge wasderived, and if the sample point is located outside the processed edge,then the smaller rectangular area, with which the sample point isassociated, is located wholly outside the edge from which the processededge was derived.
 8. (canceled)
 9. A method according to claim 8,further comprising outputting a first value if By+C>−Ax and outputting asecond value if By+C<−Ax, one of the first value and the second valueindicating that the sample point is located inside the processed edgeand the other of the first value and the second value indicating thatthe sample point is located outside the processed edge.
 10. (canceled)11. (canceled)
 12. (canceled)
 13. A graphics system having a renderingspace divided into a plurality of rectangular areas and having eachrectangular area sub-divided into a plurality of smaller rectangularareas each comprising a plurality of pixels, the graphics systemcomprising a processing unit configured to: receive data representing atiled set of polygons to be rendered in a selected one of therectangular areas; and determine, for each polygon in the tiled set,whether that polygon is located at least partially inside a selected oneof the smaller rectangular areas in the selected rectangular area; andwherein the processing unit is configured to determine whether thepolygon is located at least partially inside the selected smallerrectangular area by: deriving a plurality of edges from the polygondata; and comparing each of the plurality of edges with a sample pointassociated with the selected smaller rectangular area to determinewhether the selected smaller rectangular area is located wholly outsideany of the edges; wherein if the selected smaller rectangular area isnot located wholly outside any of the edges then the polygon isdetermined to be located at least partially inside the selected smallerrectangular area; wherein, if that polygon is located at least partiallyinside the selected smaller rectangular area, the processing unit isarranged to determine which of the plurality of pixels in the selectedsmaller rectangular area are inside the polygon, and if that polygon isnot located at least partially inside the selected smaller rectangulararea, the processing unit is arranged to perform no further processingof the polygon at one or more of the plurality of pixels in the smallerrectangular area.
 14. A graphics system according to claim 13, whereinthe processing unit is further configured to: receive a plurality ofimage polygons to be rendered in the rendering space; and tile the imagepolygons to generate the tiled set of polygons by determining at leastthose image polygons that are located within the selected rectangulararea.
 15. A graphics system according to claim 13, wherein theprocessing unit is configured to compare each of the plurality of edgesby: processing each of the plurality of edges to derive a plurality ofprocessed edges, wherein the processing comprises, for each edge,determining an orientation of the respective edge and applying atranslation to the respective edge in accordance with the orientation;comparing each of the plurality of processed edges with the samplepoint.
 16. A graphics system according to claim 15, wherein theprocessing unit is configured to apply the translation to the respectiveedge in accordance with the orientation by: applying a translation tothe respective edge in one dimension, applying a translation to therespective edge in two dimensions, or applying no translation to therespective edge.
 17. (canceled)
 18. A graphics system according to claim17, wherein the processing unit is configured to use the determinationof whether the evaluation exceeds a predetermined threshold to determinewhether the sample point is located inside or outside the processededge.
 19. A graphics system according to claim 18, wherein if the samplepoint is located inside the processed edge, then the smaller rectangulararea, with which the sample point is associated, is located at leastpartially inside the edge from which the processed edge was derived, andif the sample point is located outside the processed edge, then thesmaller rectangular area, with which the sample point is associated, islocated wholly outside the edge from which the processed edge wasderived.
 20. (canceled)
 21. A graphics system according to claim 20,wherein the processing unit is configured to output a first value ifBy+C>−Ax and output a second value if By+C<−Ax, one of the first valueand the second value indicating that the sample point is located insidethe processed edge and the other of the first value and the second valueindicating that the sample point is located outside the processed edge.22. (canceled)
 23. (canceled)
 24. (canceled)
 25. (canceled) 26.(canceled)
 27. (canceled)
 28. A graphics processing unit configured torender to a rendering space divided into a plurality of rectangularareas, each rectangular area being sub-divided into a plurality ofsmaller rectangular areas each comprising a plurality of pixels, thegraphics processing unit comprising: an interface to a memory device; amicrotiling unit arranged to receive via the interface data representinga tiled set of polygons to be rendered in a selected one of therectangular areas, determine for each smaller rectangular area in theselected rectangular area whether that smaller rectangular area containsat least a portion of a selected polygon, and output a correspondingindication; and a scan converter configured to receive the indications,and if a selected one of the smaller rectangular areas contains at leasta portion of the selected polygon, determine which of the plurality ofpixels in the respective smaller rectangular area are inside theselected polygon, and if a selected one of the smaller rectangular areasdoes not contain at least a portion of the selected polygon, perform nofurther processing of the selected polygon at one or more of theplurality of pixels in the respective smaller rectangular area; whereinthe microtiling unit comprises edge calculation logic configured toreceive the selected polygon and derive a plurality of edge equationparameters for each edge of the selected polygon and edge processinglogic coupled to the edge calculation logic and configured to receivethe plurality of edge equation parameters for a selected edge of theselected polygon and to determine an orientation of the selected edgeand apply a translation to the edge equation parameters in accordancewith the orientation to generate processed edge equation parameters,wherein the translation corresponds to a shift of the selected edge inone dimension, two dimensions, or no shift of the selected edge; andoutput the processed edge equation parameters.
 29. A graphics processingunit according to claim 28, further comprising: a tiling unit configuredto receive a plurality of image polygons to be rendered in the renderingspace, tile the image polygons to generate the tiled set of polygons bydetermining at least those image polygons that are located at leastpartially within the selected rectangular area, and output the tiled setof polygons to the memory device.
 30. A graphics processing unitaccording to claim 28, wherein the edge processing logic comprises aquadrant determination unit arranged to determine the orientation of theselected edge of the polygon by evaluating the signs of one or more ofthe edge equation parameters.
 31. (canceled)
 32. A graphics processingunit according to claim 31, wherein the comparison unit is furtherconfigured to: perform the determination of which of the smallerrectangular areas are located wholly outside the selected edge of thepolygon, and which are located at least partially inside the selectededge of the polygon for each edge of the selected polygon; and generatethe indication such that any of the smaller rectangular areas that arenot located wholly outside at least one edge of the selected polygon areindicated as containing at least a portion of a selected polygon.
 33. Agraphics processing unit according to claim 31, wherein the comparisonunit comprises: one or more evaluation units configured to receive theprocessed edge equation parameters and generate a first value from theprocessed edge equation parameters for each of the smaller rectangularareas in dependence on its position in the rectangular area, and asecond value from the processed edge equation parameters for each of thesmaller rectangular areas in dependence on its position in therectangular area.
 34. A graphics processing unit according to claim 33,wherein the comparison unit further comprises: a clamping unitconfigured to receive the first value and generate a reduced first valueby reducing the precision of the first value in dependence on the numberof bits used to represent the second value.
 35. A graphics processingunit according to claim 33, wherein the comparison unit furthercomprises: a comparator array comprising a plurality of comparators eachassociated with at least one of the smaller rectangular areas andconfigured to operate in parallel, each comparator configured to comparethe first value or the reduced first value with the second value for itsrespective smaller rectangular area to determine whether that smallerrectangular area is located wholly outside the selected edge of thepolygon or located at least partially inside the selected edge of thepolygon. 36-55. (canceled)